859 research outputs found
A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions
We introduce a framework based on Rockafellar's perturbation theory to
analyze and solve general nonsmooth convex minimization and monotone inclusion
problems involving nonlinearly composed functions as well as linear
compositions. Such problems have been investigated only from a primal
perspective and only for nonlinear compositions of smooth functions in
finite-dimensional spaces in the absence of linear compositions. In the context
of Banach spaces, the proposed perturbation analysis leads to the construction
of a dual problem and of a maximally monotone Kuhn--Tucker operator which is
decomposable as the sum of simpler monotone operators. In the Hilbertian
setting, this decomposition leads to block-iterative primal-dual proximal
algorithms that fully split all the components of the problem and capture
state-of-the-art existing methods as special cases
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